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I wonder why a DoE/fractional factorial design isn't studied with the help of a linear mixed model? Or an Anova? How to analyze it in general is e.g. given here.

Background: I will study several gas sensors to select the "best" one. Best one means the one that provides the fastest reaction time, most clear and distinct signal and also shows the least influence from different gases.

Ben
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  • Not studied with linear model or anova... It isn't? – Sextus Empiricus Sep 20 '19 at 13:10
  • mh, ok.. so DoE is "only" for planning the design? – Ben Sep 20 '19 at 13:26
  • Voting to close as unclear because nowhere in the cited references does anything claim such an experiment can't analyzed with linear model (which is equivalent to ANOVA BTW). – AdamO Sep 20 '19 at 13:40
  • a linear model is equivalent to anova? – Ben Sep 20 '19 at 13:55
  • Can you please add (as an edit to the Q) which factors you control in that gas sensor experiment, other details (like number of sensors, number of runs ...), and which factors cannot be controlled in actual use, but only in the experiment? – kjetil b halvorsen Sep 20 '19 at 13:58
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    I am voting to close because you seem to have a lot of questions, which currently seem to be dumped all into one question. The people here are willing to answer all those questions but it is not the point of this website to become a chatbox for discussions. The point is that we wish to have clear (concise) questions and answers that will have also use in the future for people with the same questions. That means that the particular issues need to be well described and isolated for other people to be able to find them (contrary to find a way in a bewildered forest of questions). – Sextus Empiricus Sep 20 '19 at 14:52

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This is overly broad, for more useful answers tell us some context, or your intended application (with sufficient detail.) For your implied question in a comment, yes DoE (Design of Experiment) is about the planning, that is, actually to be done before you actually do the experiment. Linear mixed models are used if you have some random factors, for example, in a Taguchi designs these could be ambient factors that can be controlled in an experiment, but not in production.

So there is certainly the possibility to use mixed models for data obtained from designed experiments, but the need for that comes from the actual application, and not from the design.

kjetil b halvorsen
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  • thanks a lot for clearing my questions. Which question would lead to mixed models? I updated my question. – Ben Sep 20 '19 at 13:53
  • @kjetil: Sorry for the necro If I may bother you, can you please point me to a ref for the group structure associated to a fractional design: I ( think I) understand that the aliasing brings about the relations, but would be great if I could see a specifically worked example. – MSIS Feb 24 '24 at 03:52
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    @MSIS: I would start with the Box, Hunter & Hunter referenced at https://stats.stackexchange.com/a/103848/11887 Many worked examples there – kjetil b halvorsen Feb 24 '24 at 04:46